the empirical foundation of the golden rule

The empirical
Estudios
de Economía.
foundation
Vol.
of28
the- golden
Nº 1, Junio
rule /2001.
VíctorPágs.
J. Elías
79-88
79
THE EMPIRICAL FOUNDATION OF THE
GOLDEN RULE
VÍCTOR J. ELÍAS*
Abstract
This working paper analizes with cross-sectional data if the Golden Rule condition satisfies: where the saving index is equal to capital (β) or to the real
interest rate, equal to the gross output growth of households.
Resumen
Este paper analiza con datos de corte transversal si se cumple la condición de
la Regla de Oro: donde el índice de ahorro es igual al capital (β), o el tipo de
interés real (i), igual al crecimiento bruto del producto de los hogares.
Se analizarán las implicancias que podría tener ésta, para la pérdida de eficacia
o bienestar.
JEL: E60, E10, 011, 020.
Keywords: Development, efficiency, welfare.
I. INTRODUCTION
The Golden Rule (GR) as developed by E. Phelps (1966) gives the condition under which a country will grow maximizing its consumption per capita.
The condition is obtained when the country is growing in its long run path with
stability fulfilled.
*
I appreciate the comments of Professor Ricardo Caballero about the existence of a very
interesting literature on the empirical assessment about dynamic efficiency specially the
work of Abel-Mankiw-Summers-Zeckhauser (1989) where they use as criteria the comparison of total profits with total investment. Dynamic efficiency exist if profits are greater
than investment for a reasonable long period. They suggest that this criteria is much
better than to use the golden rule criteria. I will work also on this line than in some
respects could be similar. My impression is that we should work much more on this
empirical avenue. The suggestions of R. Cifuentes and the ones coming out from the
conference were also very useful.
■ University of Tucuman and Foundation Banco Empresario.
80
Estudios de Economía, Vol. 28 - Nº 1
The objective of this paper is to check with cross-country data if this condition provided by the GR: rate of saving (s) equal to the capital share (β), or real
interest rate (i) equal to gross domestics product growth (GDP), are actually
fulfilled. Even though these are long-run conditions could be of interest to analyze how far are they from current conditions, and what are the implications for
efficiency or welfare loss.
This very preliminar exercise will use the data provided by the World Development Indicators 2000 (World Bank) and other studies that provides estimates of β, capital growth and Total Factor Productivity (TFP). For some of the
parameters there are information for almost 150 countries, but much less of 100
of them covers all the relevant parameters.
II. DATA BEHAVIOR
In this section we present frequency distributions for real interest rate (i);
annual GDP rate of growth for the period 1965-1998 (y); capital share (β1);
share of total income of the upper 10th decile group (β2); annual capital stock
rate of growth for the period 1950-1987 (k); annual Total Factor Productivity
rate of growth for the period 1950-1987 (g); acceleration of the rate of change
of the GDP (∆y) between the 90’s with respect to the 80’s.
FIGURE A
FREQUENCY OF DISTRIBUTION OF THE VARIABLES AND “PARAMETERS”
A.1. Frequency Distribution of Real Rate
Interest 1998 (i)
A.2. Frequency Distribution of GDP Rate
of Change 65-98 (y)
25
14
12
20
10
15
8
6
10
4
5
2
0
0
-25.0
-12.5
0.0
12.5
25.0
37.5
50.0
Real Rate of Interest
-4
-2
0
2
4
6
8
10
GDP Rate of Change
The empirical foundation of the golden rule / Víctor J. Elías
81
FIGURE A (cont.)
FREQUENCY OF DISTRIBUTION OF THE VARIABLES AND “PARAMETERS”
A.3. Frequency Distribution of “GDP
Rate of Change 90-98 – GDP Rate
of Change 80-90” (∆y)
A.4. Frequency Distribution of Gross
Domestic Saving 1980 (s80)
25
25
20
20
15
15
10
10
5
5
0
0
-16 -14 -12 -10
-8
-6
-4
-2
0
2
4
6
-60
8
-40
-20
0
20
40
60
GDP Rate of Change 90-98 – GDP Rate of Change 80-90
Gross Domestic Saving
A.5. Frequency Distribution of Gross
Domestic Saving 1980 (s98)
A.6. Frequency Distribution of Capital
Share (β1)
25
8
20
6
15
4
10
2
5
0
0
-37.5
-25.0
-12.5
0.0
12.5
25.0
37.5
50.0
Gross Domestic Saving
20
30
40
50
60
70
80
90
Capital Share
82
Estudios de Economía, Vol. 28 - Nº 1
FIGURE A (cont.)
FREQUENCY OF DISTRIBUTION OF THE VARIABLES AND “PARAMETERS”
A.7. Frequency Distribution of Share of
Income of Top 10% (β1)
A.8. Frequency Distribution of GDP per
capita 1998 (GDP/N)
12
25
10
20
8
15
6
10
4
5
2
0
0
18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
0
4000
8000
12000
16000
20000
24000
28000
Share of Income of Top 10%
GDP per capita
A.9. Frequency Distribution of Change of
TFP 1950-87 (g)
A.10. Frequency Distribution of Capital
Rate of Growth 1950-87 (k)
10
12
8
10
8
6
6
4
4
2
2
0
0
-3
-2
-1
0
1
2
3
4
Change of TFP
-2.5
0.0
2.5
5.0
7.5
10.0
12.5
15.0
Capital Rate of Growth
The empirical foundation of the golden rule / Víctor J. Elías
83
TABLE Nº 1
SUMMARY OF THE BEHAVIOR OF MAIN VARIABLES AND “PARAMETERS”
Parameters
Mean
Standard
Deviation
Number
of
Observations
i
Real rate of interest (1998)
10.5
12.7
105
y
GDP rate of change 65-98
2.1
2.4
110
∆y
GDP rate of change 90-98 – GDP rate of change 80-90
–0.2
4.1
144
s80
Gross domestic saving 1980
19.7
17.1
113
S98
Gross domestic saving 1998
15.1
13.3
136
β1
Capital share (near 1998)
51.0
18.6
81
β2
Share of income of top 10% (near 1998)
31.1
7.6
108
6944.8
7533.8
135
Y/N GDP per capita 1998
g
Change of TFP (1950-1987)
1.1
1.4
92
k
Capita rate of growth (1950-1987)
4.8
3.0
92
III. GOLDEN RULE’S “VERIFICATION”
In this section we “verify” how close is satisfied the GR. We make the following graphical analysis:
1. How far are the countries from their long run conditions: we compare GDP
Growth (y) with the Capital Growth (k):
20
R2 = 0.34
k* ≈ 0.75 . y*
Capital rate of growth (1950-1987)
45°
15
10
5
0
-5
-5
0
5
10
GDP rate of change 65-98
15
20
84
Estudios de Economía, Vol. 28 - Nº 1
2. How far are the countries from the GR’s condition i = y (*):
Real rate of interest (1998)
60
40
45°
20
0
-20
-40
-5
0
5
10
15
20
GDP rate of change 65-98
Real rate of interest (1998)
60
40
45°
20
0
-20
-40
-5
0
5
10
15
20
GDP rate of change 65-98
“Lower GDP per capita”
60
Real rate of interest (1998)
40
45°
20
0
-20
-40
-5
0
5
10
15
20
GDP rate of change 65-98
“Upper GDP per capita”
(*) Milton Friedman (1971) in some of his estimates of demand function for money used “y”
as a proxy for “i”, based on this GR.
The empirical foundation of the golden rule / Víctor J. Elías
85
3. How far are the countries from GR’s s = β:
100
45
Gross domestic saving 1998
80
60
40
20
0
-20
-40
-60
-60
-40
-20
0
20
40
60
80
100
Capital share (near 1998)
100
45°
Gross domestic saving 1998
80
60
40
20
0
-20
-40
-60
-60
-40
-20
0
20
40
60
80
100
Capital share (near 1998)
“Lower GDP per capita”
100
45°
Gross domestic saving 1998
80
60
40
20
0
-20
-40
-60
-60
-40
-20
0
20
40
60
Capital share (near 1998)
“Upper GDP per capita”
80
100
86
Estudios de Economía, Vol. 28 - Nº 1
Gross domestic saving 1998
60
45°
40
20
0
-20
-40
-60
-60
-40
-20
0
20
40
60
Share of income of top 10% (near 1998)
60
45°
Gross domestic saving 1998
40
20
0
-20
-40
-60
-60
-40
-20
0
20
40
60
Share of income of top 10% (near 1998)
“Lower GDP per capita”
Gross domestic saving 1998
60
45°
40
20
0
-20
-40
-60
-60
-40
-20
0
20
40
Share of income of top 10% (near 1998)
“Upper GDP per capita”
60
The empirical foundation of the golden rule / Víctor J. Elías
87
IV. SOME IMPLICATIONS
As we do no get a “verification” of the GR’s we try to see if the departure
from it could be explained by:
1. If the two GR’s are consistent:
GDP rate of change – Real rate of interest
40
20
0
-20
-40
-60
-100
-80
-60
-40
-20
0
20
Gross domestic saving – Capital share
2. If the departure of s from b are related to efficiency problems. We relate
s – β with TFP growth:
Gross domestic saving – Capital share
20
0
-20
-40
-60
-80
-100
-4
-2
0
2
Change of TFP (1950-1987)
4
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Estudios de Economía, Vol. 28 - Nº 1
Real rate interest – GDP rate of change
60
40
20
0
-20
-40
-4
-2
0
2
4
Change of TFP (1950-1987)
V.
REFERENCES
1.
Abel, Andrew, N.G. Mankiw, L. Summers and R. Zeckhauser (1989). “Assessing Dynamic Efficiency: Theory and Evidence”, Review of Economic
Studies, 56, pp. 1-20.
Elías, Víctor (1993). “The Role of Total Factor Productivity on Economic
Growth”, Estudios de Economía, Volume 20, Special Number, June.
Friedman, Milton (March-April 1971). “A Monetary Theory of Nominal
Income”, Journal of Political Economy, 79, pp. 323-37.
Gollin, Douglas (1998). “Getting Income Shares Right: Self-Employment,
Unincorporated Enterprise, and the Cobb-Douglas Hypothesis”, draft,
Williams College, Williamstown, Department of Economics.
Phelps, Edmund (1966). Golden Rules of Economic Growth, New York,
Norton.
The World Bank (2000), World Development Indicators World Bank 2000,
Washington D.C.
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3.
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5.
6.